Finite Group Databasebeta

← #28496668

Subgroups — #28496668

Order 15104.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273660C211yesmaximal, characteristic
2C2×#16837164C211yesmaximal, characteristic
3C2×#16837164C211yesmaximal, characteristic
4C2×#16837164C211yesmaximal, characteristic
5C2×#16837157C211yesmaximal, characteristic
6#21422326C211yesmaximal, characteristic
7C2×C59×#389C211yesmaximal, characteristic
8C23×C59⋊C8C2211yescharacteristic
9C23×C59⋊C8C2211yescharacteristic
10C22×C4⋊Dic59C2211yescharacteristic
11C22×C4⋊Dic59C2211yescharacteristic
12C2×#14273660—22no—
13C2×#14273660—22no—
14C2×#14273660C414yescomplemented
15C2×C59⋊#95—21no—
16C2×C59⋊#95—21no—
17#16837164—22no—
18#16837164—22no—
19#16837164—22no—
20#16837157—22no—
21C22×C4⋊C4×C59—21no—
22C22×C4⋊C4×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C42×C59C2211yescharacteristic
25C59×#389—22no—
26C59×#389—22no—
27C2×#95×C59—21no—
28C23×Dic59—21no—
29C23×Dic59—21no—
30C22×C59⋊C8—21no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36C22×C59⋊C8—21no—
37C22×C59⋊C8—21no—
38C22×C59⋊C8—21no—
39C22×C59⋊C8—21no—
40C22×C59⋊C8C2×C412yes—
41C22×C59⋊C8D412yes—
42C22×C59⋊C8Q812yes—
43C22×C59⋊C8Q812yes—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59—21no—
50C2×C4⋊Dic59—21no—
51C2×C4⋊Dic59—21no—
52C2×C4⋊Dic59—21no—
53C2×C4⋊Dic59—21no—
54C2×C4⋊Dic59C2×C412yes—
55C2×C4⋊Dic59Q812yes—
56#14273660—28no—
57C59⋊#95—42no—
58C59⋊#95—42no—
59C23×C4×C59—21no—
60C23×C4×C59—21no—
61C23×C4×C59D411yescharacteristic
62C23×C4×C59D411yescharacteristic
63C23×C4×C59C2311yescharacteristic
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C4⋊C4×C59—21no—
67C2×C4⋊C4×C59—21no—
68C2×C4⋊C4×C59—21no—
69C2×C4⋊C4×C59—21no—
70C2×C4⋊C4×C59—21no—
71C2×C4⋊C4×C59—24no—
72C2×C4⋊C4×C59—21no—
73C2×C4⋊C4×C59—42no—
74C2×C4⋊C4×C59—42no—
75C2×C4⋊C4×C59C2×C412yes—
76C2×C4⋊C4×C59D412yes—
77C2×C4⋊C4×C59D412yes—
78C2×C4⋊C4×C59D412yes—
79C2×C42×C59—21no—
80C2×C42×C59—21no—
81C2×C42×C59—21no—
82C2×C42×C59—21no—
83C2×C42×C59—21no—
84C2×C42×C59—21no—
85#95×C59—24no—
86C24×C59C2×D411yescharacteristic
87C22×C4×C59—22no—
88C22×C4×C59—21no—
89C22×C4×C59—22no—
90C22×C4×C59—21no—
91C22×C4×C59—21no—
92C22×C4×C59—21no—
93C22×C4×C59—22no—
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—21no—
99C22×C4×C59—21no—
100C22×C4×C59—21no—
101C22×C4×C59—21no—
102C22×C4×C59—22no—
103C22×C4×C59—41no—
104C22×C4×C59—41no—
105C22×C4×C59—41no—
106C22×C4×C59—41no—
107C22×C4×C59—41no—
108C22×C4×C59—41no—
109C22×C4×C59—41no—
110C22×C4×C59—41no—
111C22×C4×C59—41no—
112C22×C4×C59—41no—
113C22×C4×C59D812yes—
114C22×C4×C59Q1612yes—
115C22×C4×C59C22×C411yescharacteristic
116C22×C4×C59C2×D411yescharacteristic
117C22×C4×C59C2×D411yescharacteristic
118C22×C4×C59C2×D411yescharacteristic
119C22×C4×C59C2×D411yescharacteristic
120C22×C4×C59C2×Q811yescharacteristic
121C22×C4×C59C2×Q811yescharacteristic
122C22×C4×C59C2×Q811yescharacteristic
123C22×C4×C59#4111yescharacteristic
124C22×C4×C59#4111yescharacteristic
125C22×C4×C59#4111yescharacteristic
126C22×C4×C59#4111yescharacteristic
127C22×C4×C59#4111yescharacteristic
128C22×C4×C59#4111yescharacteristic
129C22×Dic59—22no—
130C22×Dic59—22no—
131C22×Dic59—41no—
132C22×Dic59—41no—
133C22×Dic59—41no—
134C22×Dic59—41no—
135C22×Dic59—41no—
136C22×Dic59—41no—
137C22×Dic59—41no—
138C22×Dic59—41no—
139C22×Dic59—41no—
140C22×Dic59—41no—
141C22×Dic59—41no—
142C22×Dic59—41no—
143C4⋊C4×C59—22no—
144C4⋊C4×C59—22no—
145C4⋊C4×C59—22no—
146C4⋊C4×C59—22no—
147C4⋊C4×C59—22no—
148C4⋊C4×C59—48no—
149C4⋊C4×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59C22⋊C414yes—
152C42×C59—41no—
153C42×C59—41no—
154C42×C59—41no—
155C42×C59—41no—
156C4⋊Dic59—22no—
157C4⋊Dic59—22no—
158C4⋊Dic59—22no—
159C4⋊Dic59—22no—
160C4⋊Dic59—41no—
161C4⋊Dic59—41no—
162C4⋊Dic59—41no—
163C4⋊Dic59—41no—
164C2×C59⋊C8—22no—
165C2×C59⋊C8—22no—
166C2×C59⋊C8—22no—
167C2×C59⋊C8—22no—
168C2×C59⋊C8—22no—
169C2×C59⋊C8—22no—
170C2×C59⋊C8—22no—
171C2×C59⋊C8—22no—
172C2×C59⋊C8—22no—
173C2×C59⋊C8—41no—
174C2×C59⋊C8—41no—
175C2×C59⋊C8—41no—
176C2×C59⋊C8—41no—
177C2×C59⋊C8C4⋊C414yescomplemented
178C23×C59C4×D411yescharacteristic
179C23×C59#12011yescharacteristic
180C23×C59#12111yescharacteristic
181C23×C59#12111yescharacteristic
182C23×C59C22⋊Q811yescharacteristic
183C23×C59#12311yescharacteristic
184C23×C59C4⋊Q811yescharacteristic
185C23×C59C2×D811yescharacteristic
186C23×C59C2×Q1611yescharacteristic
187C23×C59#13511yescharacteristic
188C23×C59#13511yescharacteristic
189C23×C59AGL(1,ℤ/8)11yescharacteristic
190C23×C59AGL(1,ℤ/8)11yescharacteristic
191C23×C59#13711yescharacteristic
192C23×C59#13711yescharacteristic
193C2×C4×C59—24no—
194C2×C4×C59—22no—
195C2×C4×C59—22no—
196C2×C4×C59—22no—
197C2×C4×C59—22no—
198C2×C4×C59—22no—
199C2×C4×C59—22no—
200C2×C4×C59—41no—
201C2×C4×C59—41no—
202C2×C4×C59—42no—
203C2×C4×C59—42no—
204C2×C4×C59—42no—
205C2×C4×C59—41no—
206C2×C4×C59—42no—
207C2×C4×C59—41no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—41no—
213C2×C4×C59—41no—
214C2×C4×C59—42no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—81no—
218C2×C4×C59—81no—
219C2×C4×C59—81no—
220C2×C4×C59—81no—
221C2×C4×C59C2×C22⋊C411yescharacteristic
222C2×C4×C59C2×C4⋊C411yescharacteristic
223C2×C4×C59#11711yescharacteristic
224C2×C4×C59C4×D411yescharacteristic
225C2×C4×C59C4×Q811yescharacteristic
226C2×C4×C59C4×Q811yescharacteristic
227C2×C4×C59#12111yescharacteristic
228C2×C4×C59#12111yescharacteristic
229C2×C4×C59#12111yescharacteristic
230C2×C4×C59#12111yescharacteristic
231C2×C4×C59C22⋊Q811yescharacteristic
232C2×C4×C59C22⋊Q811yescharacteristic
233C2×C4×C59C22⋊Q811yescharacteristic
234C2×C4×C59C22⋊Q811yescharacteristic
235C2×C4×C59C22⋊Q811yescharacteristic
236C2×C4×C59C22⋊Q811yescharacteristic
237C2×C4×C59C22⋊Q811yescharacteristic
238C2×C4×C59#12311yescharacteristic
239C2×C4×C59#12311yescharacteristic
240C2×C4×C59#12411yescharacteristic
241C2×C4×C59#12511yescharacteristic
242C2×C4×C59#12511yescharacteristic
243C2×C4×C59#12511yescharacteristic
244C2×C4×C59#12511yescharacteristic
245C2×C4×C59#12611yescharacteristic
246C2×C4×C59#12611yescharacteristic
247C2×C4×C59C4⋊Q811yescharacteristic
248C2×C4×C59C4⋊Q811yescharacteristic
249C2×Dic59—42no—
250C2×Dic59—42no—
251C2×Dic59—42no—
252C2×Dic59—42no—
253C2×Dic59—42no—
254C2×Dic59—42no—
255C2×Dic59—81no—
256C2×Dic59—81no—
257C2×Dic59—81no—
258C2×Dic59—81no—
259C2×Dic59—81no—
260C2×Dic59—81no—
261C2×Dic59—81no—
262C2×Dic59—81no—
263C59⋊C8—24no—
264C59⋊C8—42no—
265#11219—591nomaximal, Sylow
266C22×C59#38611yescharacteristic
267C22×C59#38711yescharacteristic
268C22×C59#38911yescharacteristic
269C22×C59#39411yescharacteristic
270C22×C59#39511yescharacteristic
271C22×C59#39611yescharacteristic
272C22×C59#39811yescharacteristic
273C22×C59C4×D811yescharacteristic
274C22×C59C4×Q1611yescharacteristic
275C22×C59#44111yescharacteristic
276C22×C59#44211yescharacteristic
277C22×C59#44711yescharacteristic
278C22×C59#44911yescharacteristic
279C22×C59#45111yescharacteristic
280C22×C59#45211yescharacteristic
281C22×C59#45911yescharacteristic
282C22×C59#46211yescharacteristic
283C22×C59#46311yescharacteristic
284C22×C59#46411yescharacteristic
285C22×C59#46611yescharacteristic
286C22×C59#46711yescharacteristic
287C22×C59#46811yescharacteristic
288C22×C59#46811yescharacteristic
289C22×C59#47411yescharacteristic
290C22×C59#47711yescharacteristic
291C22×C59#47811yescharacteristic
292C22×C59#47911yescharacteristic
293C22×C59#48011yescharacteristic
294C22×C59#48211yescharacteristic
295C22×C59#48411yescharacteristic
296C22×C59#48511yescharacteristic
297C22×C59#49911yescharacteristic
298C22×C59#50011yescharacteristic
299C22×C59#50111yescharacteristic
300C22×C59#50111yescharacteristic
301C4×C59—44no—
302C4×C59—42no—
303C4×C59—42no—
304C4×C59—82no—
305C4×C59#38011yescharacteristic
306C4×C59#38711yescharacteristic
307C4×C59#38911yescharacteristic
308C4×C59#39111yescharacteristic
309C4×C59#39611yescharacteristic
310C4×C59#39811yescharacteristic
311C4×C59#39811yescharacteristic
312C4×C59#40011yescharacteristic
313Dic59—82no—
314Dic59—82no—
315C22×#107—591no—
316C2×#389D5911yescharacteristic
317C2×#340—591no—
318C2×#340—591no—
319C2×#340—591no—
320C2×#336—591no—
321C4⋊#95—591no—
322C2×C59#144111yescharacteristic
323C2×C59#187811yescharacteristic
324C2×C59#187911yescharacteristic
325C2×C59#191811yescharacteristic
326C2×C59#192111yescharacteristic
327C2×C59#194211yescharacteristic
328C2×C59#194311yescharacteristic
329C2×C59#203311yescharacteristic
330C2×C59#203611yescharacteristic
331C2×C59#205711yescharacteristic
332C2×C59#205911yescharacteristic
333C2×C59#206711yescharacteristic
334C2×C59#206811yescharacteristic
335C2×C59#208311yescharacteristic
336C2×C59#208511yescharacteristic
337C23×C8—591no—
338C23×C8—591no—
339C22×C4⋊C4—21no—
340C22×C4⋊C4—591no—
341C22×C4⋊C4—591no—
342C22×C4⋊C4C2×D5911yescharacteristic
343C22×C4⋊C4C2×D5911yescharacteristic
344C22×C42C2×D5911yescharacteristic
345C2×#107—594no—
346C2×#107—1182no—
347C2×#107—1182no—
348#389—22no—
349#389—22no—
350C2×#95—21no—
351C2×#95—1181no—
352C2×#95—1181no—
353#340—1182no—
354#340—1182no—
355#340—1182no—
356#336—1182no—
357C59#1121911yescharacteristic, complemented, Sylow
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—1181no—
361C23×C4—1181no—
362C23×C4C22⋊D5911yescharacteristic
363C23×C4C22⋊D5911yescharacteristic
364C23×C4C22×D5911yescharacteristic
365C22×C8—592no—
366C22×C8—592no—
367C22×C8—592no—
368C22×C8—592no—
369C22×C8—1181no—
370C22×C8—1181no—
371C22×C8—1181no—
372C22×C8—1181no—
373C22×C8—1181no—
374C22×C8—1181no—
375C22×C8—1181no—
376C22×C8—1181no—
377C22×C8—1181no—
378C22×C8—1181no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—592no—
391C2×C4⋊C4—592no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4—1181no—
395C2×C4⋊C4—1181no—
396C2×C4⋊C4—1181no—
397C2×C4⋊C4—1181no—
398C2×C4⋊C4—1181no—
399C2×C4⋊C4—1181no—
400C2×C4⋊C4—1181no—
401C2×C4⋊C4—1181no—
402C2×C4⋊C4C4×D5912yes—
403C2×C4⋊C4D23612yes—
404C2×C4⋊C4C22⋊D5912yes—
405C2×C4⋊C4C22⋊D5912yes—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412#107—1188no—
413#95—24no—
414#95—2362no—
415#95—2362no—
416C24C2×C22⋊D5911yescharacteristic
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—1182no—
444C22×C4—1182no—
445C22×C4—2361no—
446C22×C4—2361no—
447C22×C4—2361no—
448C22×C4—2361no—
449C22×C4—2361no—
450C22×C4—2361no—
451C22×C4—2361no—
452C22×C4—2361no—
453C22×C4—2361no—
454C22×C4—2361no—
455C22×C4—2361no—
456C22×C4—2361no—
457C22×C4#1174566912yes—
458C22×C4#1174567212yes—
459C22×C4C2×C4×D5911yescharacteristic
460C22×C4C2×D23611yescharacteristic
461C22×C4#1174568511yescharacteristic
462C22×C4#1174568511yescharacteristic
463C22×C4D4×D5911yescharacteristic
464C22×C4#1174568711yescharacteristic
465C22×C4#1174568711yescharacteristic
466C22×C4#1174568711yescharacteristic
467C22×C4Q8×D5911yescharacteristic
468C22×C4Q8×D5911yescharacteristic
469C22×C4Q8×D5911yescharacteristic
470C22×C4#1174568911yescharacteristic
471C22×C4C2×C22⋊D5911yescharacteristic
472C22×C4C2×C22⋊D5911yescharacteristic
473C2×C8—594no—
474C2×C8—1182no—
475C2×C8—1182no—
476C2×C8—1182no—
477C2×C8—1182no—
478C2×C8—1182no—
479C2×C8—1182no—
480C2×C8—1182no—
481C2×C8—1182no—
482C2×C8—1182no—
483C2×C8—2361no—
484C2×C8—2361no—
485C2×C8—2361no—
486C2×C8—2361no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—48no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—1182no—
496C4⋊C4—1182no—
497C4⋊C4—1182no—
498C4⋊C4—1182no—
499C4⋊C4—2361no—
500C4⋊C4—2361no—
501C4⋊C4—2361no—
502C4⋊C4—2361no—
503C4⋊C4(C2×D59)⋊C414yes—
504C42—41no—
505C42—41no—
506C42—41no—
507C42—41no—
508C23C4×C22⋊D5911yescharacteristic
509C23#1427369611yescharacteristic
510C23#1427369911yescharacteristic
511C23#1427370111yescharacteristic
512C23#1427370311yescharacteristic
513C23#1427370811yescharacteristic
514C23#1427372511yescharacteristic
515C23C2×#1174566911yescharacteristic
516C23C2×#1174567211yescharacteristic
517C23#1427374711yescharacteristic
518C23#1427374711yescharacteristic
519C23#1427375211yescharacteristic
520C23#1427375311yescharacteristic
521C23#1427375711yescharacteristic
522C23#1427375811yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—4721no—
552C2×C4—4721no—
553C2×C4—4721no—
554C2×C4—4721no—
555C2×C4—4721no—
556C2×C4—4721no—
557C2×C4—4721no—
558C2×C4—4721no—
559C2×C4—2362no—
560C2×C4—2362no—
561C2×C4—2362no—
562C2×C4—2362no—
563C2×C4—2362no—
564C2×C4—2362no—
565C2×C4C2×(C2×D59)⋊C411yescharacteristic
566C2×C4C4⋊C4×D5911yescharacteristic
567C2×C4#1427368511yescharacteristic
568C2×C4C4×C22⋊D5911yescharacteristic
569C2×C4#1427369211yescharacteristic
570C2×C4#1427369211yescharacteristic
571C2×C4#1427369811yescharacteristic
572C2×C4#1427369911yescharacteristic
573C2×C4#1427370111yescharacteristic
574C2×C4#1427370211yescharacteristic
575C2×C4#1427370311yescharacteristic
576C2×C4#1427370311yescharacteristic
577C2×C4#1427370511yescharacteristic
578C2×C4#1427370511yescharacteristic
579C2×C4#1427370711yescharacteristic
580C2×C4#1427370711yescharacteristic
581C2×C4#1427370711yescharacteristic
582C2×C4#1427370811yescharacteristic
583C2×C4#1427371011yescharacteristic
584C2×C4#1427371411yescharacteristic
585C2×C4#1427371711yescharacteristic
586C2×C4#1427371711yescharacteristic
587C2×C4#1427371711yescharacteristic
588C2×C4#1427371711yescharacteristic
589C2×C4#1427372211yescharacteristic
590C2×C4#1427372211yescharacteristic
591C2×C4#1427372511yescharacteristic
592C2×C4#1427372511yescharacteristic
593C8—1184no—
594C8—2362no—
595C22#1683728111yescharacteristic
596C22#1683728311yescharacteristic
597C22#1683729711yescharacteristic
598C22#1683731611yescharacteristic
599C22#1683732111yescharacteristic
600C22#1683732411yescharacteristic
601C22#1683733211yescharacteristic
602C22C4×#1174566911yescharacteristic
603C22C4×#1174567211yescharacteristic
604C22#1683750711yescharacteristic
605C22#1683751211yescharacteristic
606C22#1683753611yescharacteristic
607C22#1683754711yescharacteristic
608C22#1683755811yescharacteristic
609C22#1683756411yescharacteristic
610C22#1683759711yescharacteristic
611C22#1683761211yescharacteristic
612C22#1683761711yescharacteristic
613C22#1683762411yescharacteristic
614C22#1683763611yescharacteristic
615C22#1683764111yescharacteristic
616C22#1683764611yescharacteristic
617C22#1683765011yescharacteristic
618C22#1683767911yescharacteristic
619C22#1683769411yescharacteristic
620C22#1683769911yescharacteristic
621C22#1683770611yescharacteristic
622C22#1683771311yescharacteristic
623C22#1683772311yescharacteristic
624C22#1683773511yescharacteristic
625C22#1683774011yescharacteristic
626C22#1683780111yescharacteristic
627C22#1683780511yescharacteristic
628C22#1683780811yescharacteristic
629C22#1683781211yescharacteristic
630C4—44no—
631C4—42no—
632C4—42no—
633C4—82no—
634C4—4722no—
635C4—4722no—
636C4#1683725911yescharacteristic
637C4#1683728311yescharacteristic
638C4#1683729711yescharacteristic
639C4#1683730711yescharacteristic
640C4#1683732411yescharacteristic
641C4#1683733211yescharacteristic
642C4#1683733311yescharacteristic
643C4#1683734011yescharacteristic
644C2#2142234611yescharacteristic
645C2#2142443711yescharacteristic
646C2#2142444411yescharacteristic
647C2#2142466411yescharacteristic
648C2#2142468511yescharacteristic
649C2#2142482611yescharacteristic
650C2#2142483111yescharacteristic
651C2#2142527511yescharacteristic
652C2#2142529611yescharacteristic
653C2#2142542111yescharacteristic
654C2#2142543111yescharacteristic
655C2#2142548111yescharacteristic
656C2#2142548811yescharacteristic
657C2#2142556711yescharacteristic
658C2#2142557711yescharacteristic
subgroupG/H
centerC24C2×C22⋊D59
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#389C2
socle, prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenterC2×#389D59
hypocenterC59#11219
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
14. C2×#14273660C4semidirect
177. C2×C59⋊C8C4⋊C4semidirect
357. C59#11219semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#142736602
C2×#168371642
C2×#168371572
#214223262
C2×C59×#3892
#1121959